Patients who receive transplants are at risk for lymphomas (glandular cancers) that are usually caused by Epstein-Barr virus (EBV), mainly because the medications given to prevent rejection (immunosuppressive medications) also interfere with the body's ability to fight EBV. In addition, children are especially susceptible to infections with EBV, because their immune systems generally have no experience in dealing with EBV (i.e. they have no antibodies against the virus. Antibodies are proteins our bodies make to help us fight infections). We will check all liver transplant recipients at Children's Memorial Hospital for antibodies against EBV, and then, by chance (randomly, like by flipping a coin) assign the ones who don't have EBV antibodies to a treatment that may be able to provide these antibodies passively (in other words, without them actually experiencing an EBV infection). Our goal is to determine if this treatment (Cytogam) can prevent the development of post-transplant lymphomas. Enrolling in our study may directly help the patients who receive Cytogam if we prevent EBV infections from leading to post-transplant lymphomas in those patients. It will certainly help future patients in deciding whether Cytogam is of any benefit in preventing complications of EBV infection in patients without antibodies to the virus.